Related papers: On the reaction rate constants that enable multist…
The distributive sequential n-site phosphorylation/dephosphorylation system is an important building block in networks of chemical reactions arising in molecular biology, which has been intensively studied. In the nice paper of Wang and…
Multisite phosphorylation networks are encountered in many intracellular processes like signal transduction, cell-cycle control or nuclear signal integration. In this contribution networks describing the phosphorylation and…
The parameter region of multistationarity of a reaction network contains all the parameters for which the associated dynamical system exhibits multiple steady states. Describing this region is challenging and remains an active area of…
Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
Multisite phosphorylation is a signaling mechanism well known to give rise to multiple steady states, a property termed multistationarity. When phosphorylation occurs in a sequential and distributive manner, we obtain a family of networks…
The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a…
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect…
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In…
Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…
We apply tools from real algebraic geometry to the problem of multistationarity of chemical reaction networks. A particular focus is on the case of reaction networks whose steady states admit a monomial parametrization. For such systems we…
Given a real sparse polynomial system, we present a general framework to find explicit coefficients for which the system has more than one positive solution, based on the recent article by Bihan, Santos and Spaenlehauer. We apply this…
Multisite protein phosphorylation plays a prominent role in intracellular processes like signal transduction, cell-cycle control and nuclear signal integration. Many proteins are phosphorylated in a sequential and distributive way at more…
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…
A multistationarity region is the part of a reaction network's parameter space that gives rise to multiple steady states. Mathematically, this region consists of the positive parameters for which a parametrized family of polynomial…
Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the…
Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological…
Much attention has been focused in recent years on the following algebraic problem arising from applications: which chemical reaction networks, when taken with mass-action kinetics, admit multiple positive steady states? The interest behind…
The multiple futile cycle is a phosphorylation system in which a molecular substrate might be phosphorylated sequentially n times by means of an enzymatic mechanism. The system has been studied mathematically using reaction network theory…